There are three numbers in the ratio of 3:5:7 and the sum of these numbers is…
2022
There are three numbers in the ratio of 3:5:7 and the sum of these numbers is 975. Find the three numbers.
Answer: A. 195, 325, 455 — ConceptIn a ratio a:b:c, write the quantities as ax, bx, and cx. Their total is (a+b+c)x, so one ratio part equals the total divided by a+b+c. ApplicationLet…
- A.
195, 325, 455
- B.
325, 195, 455
- C.
195, 310, 470
- D.
205, 315, 455
Attempted by 15 students.
Show answer & explanation
Correct answer: A
Concept
In a ratio a:b:c, write the quantities as ax, bx, and cx. Their total is (a+b+c)x, so one ratio part equals the total divided by a+b+c.
Application
Let the three numbers be 3x, 5x, and 7x.
Their sum gives 3x + 5x + 7x = 975, so 15x = 975.
Therefore x = 975 / 15 = 65.
The numbers are 3×65 = 195, 5×65 = 325, and 7×65 = 455.
Cross-check
Their sum is 195 + 325 + 455 = 975, and dividing all three numbers by 65 gives 3:5:7.
Result
Hence, the three numbers are 195, 325, and 455.